Magnetic field tuning of the valley population in the Weyl phase of Nd$_2$Ir$_2$O$_7$

The frustrated magnet Nd$_2$Ir$_2$O$_7$, where strong correlations together with spin-orbit coupling play a crucial role, is predicted to be a Weyl semimetal and to host topological pairs of bulk Dirac-like valleys. Here we use an external magnetic field to manipulate the localized rare earth 4f moments coupled to the 5d electronic bands. Low energy optical spectroscopy reveals that a field of only a few teslas suffices to create charge compensating pockets of holes and electrons in different regions of momentum space, thus introducing a valley population shift that can be tuned with the field.